JOP - Vol.6, n. 2. 1989 The Lie group of automorphisms of a principal bundle M.C. ABBATI, R. CIRELU, A. MANIA’ Dipaxtimento di Fisica, Università di Milano, Italy and Istituto Nazionale di Fisica Nucleare, Sezione di Milano, Italy P. MICHOR Institut für Mathematik, Universitat Wien, Austria Abstract. A convenient structure of Lie group to the entire group Aut P of G- automorphisms of a principal G-bundle without any assumption of compactness on the structure group G or on the base manifold. Its Lie algebra and the expo. nential map are illustrated. Some relevant principal bundles are discussed having A ut P or its subgroup Gau P of gauge transformations as structure group. 1. INTRODUCTION lnfmite dimensional Lie groups or infinite dimensional Lie algebras are nowa- days understood as unavoidable tools in the formulation of theories of funda- mental interactions. The group DiffM of diffeomorphisms of a manifold M is quite familiar since long time to people working in General Relativity. More recently the group Gau P of the gauge transformations of a principal bundle (P, p, M, G) gained a similar popularity among people working in Yang-Mills theories. Convenient smoothness structure for these groups have been proposed along with realizations of their Lie algebras and properties of the exponential map have been investigated ([1,2, 3]and references therein, [4,5,6,7,8]). Key-Words: Principal Bundles, Groups of Au tomorphisms. 1980 MSC: 22E, 57520